Bogomolʹnyi bounds and Killing spinors in d = 3 supergravity

We discuss the connection between the construction of Bogomolʹnyi bounds and equations in three dimensional gravitational theories and the existence of an underlying N = 2 local supersymmetric structure. We show that, apart from matter self duality equations, a first order equation for the gravitational field (whose consistency condition gives the Einstein equation) can be written as a consequence of the local supersymmetry. Its solvability makes possible the evasion of the no-go scenario for the construction of Killing spinors in asymptotically conical spacetimes. In particular we show that the existence of non-trivial supercovariantly constant spinors is guaranteed whenever field configurations saturate the topological bound.